389
1 INTRODUCTION
There are many advanced modern dynamic
positioning and autopilot systems, most of them
basedonKalmanfiltering[1],howeverthesesystems
usually require multiple sensors that provide
parameters with a good accuracy. In specific
conditions these measurements are sometimes
difficult or impossible to measure or compute.
Environmental forces
such as waves, wind and
current cause the vessel to drift. These forces are
usually separated into wave‐ and low‐frequency
components[2]andmanyinvestigationsaredevoted
forestimatingtheeffectsofwaves,windandcurrent
forcesonashipmotion[6].Sincetherearenosensors
tomeasure
environmentalforcesactingonashipwith
sufficient accuracy, it is impossible to use feed
forwardfrom the environmental disturbances. Thus,
it can be assumed for disturbance modeling that
environmental forces are constant or at least slowly
varying [3]. However the corrections must be
implementedtoobtaintheplannedtrackof
avessel.
Inpresentedmodeltheangleofvessel’stotaldriftcan
beeffectivelyusedfortrueheadingcorrectionwitha
good accuracy. This method can be easy way to
correctdeviationsoftheactualvesseltrajectoryfrom
theplannedvesseltrajectory.
2 VESSEL’STOTALDRIFTDETERMINATION
2.1 Trueheading
determination
To determine the true heading of a ship, a local
geographical Earth‐fixed frame is used. We assume
the initial
),(
111
A
and next position of a ship
),,(
222
A
obtainedfromsatelliteaerials’positions.
ThetrueheadingTCiscalculatedfromtheformula:
),/cos(
M
arctgTC
(1)
where
,
12
,
12
.2/)(
21
M
Other relationship that can be used to determine
trueheadingis:
),/arccos(
L
dTC
where
L
d denotes the main length of base line on
boardtheshipandhasbeenpresentedinfigure1.
Application of Satellite Navigation Techniques for
Vessel’s Drift Determination in Piloting Areas
A.Blokus‐Roszkowska&M.Jurdziński
GdyniaMaritimeUniversity,Poland
ABSTRACT: The paper deals with use the satellite navigation system for increase safety of navigation in
difficult areas. There have been presented an algorithm to ship control procedure during environmental
disturbancesinnarrowpassages.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 7
Number 3
September 2013
DOI:10.12716/1001.07.03.10
390
C
A
2
(
2
,
2
)
A
1
(
1
1
)
TC
cos
M
d
L
TC - True Course
Figure 1. Base line on board the ship using two GPS
receiversfortruecoursedetermination
2.2 Courseovergrounddetermination
Animportantissueofvessels’navigationinrestricted
areasistheknowledgeofcourseoverground[5].
L
dAA
21
B
dAA
43
4321
AAAA
Figure2.TwobasesonboardusingfourGPSreceiversfor
COGdetermination
To determine the course over ground four
antennas of DGPS receivers must by used. The two
base lines
L
d
,
B
d
are installed on board as
presentedinfigure2.
For estimation the actual heading and total drift
angleduringashipmovementfoursatelliteposition
mustbeobserved.Nextwedenoteby
),(
11
1 GG
G
the fixed position of a ship at moment
,
1
t
and
by
),(
22
2 GG
G
the position of a ship after a
distance
G
d at moment
.
2
t
Time
,
12
ttt
can
be a step for repeating the procedure in algorithm.
Having in disposal four satellite aerials with given
positions
),,(
111
A
),,(
222
A
),,(
333
A
),(
444
A
at moment ,
1
t we can determine the
fixed position
1
G of a ship as a mean value of
aerials’positions:
,4/)(
4321
1
G
.4/)(
4321
1
G
(2)
Figure3.SettingoftwofixesG1andG2todeterminecourse
overground
The vessel’s course over ground COG can be
determinefromformula:
),/cos)arcsin((
12
GGGG
dCOG
(3)
or
),/)arccos((
12
GGG
dCOG
(4)
where
2/)(
21
GGG
and distance run
betweenpositions
1
G
,
2
G
:
.)(]cos)[(
22
1212
GGGGGG
d
(5)
Finallytheangleofvessel’stotaldriftisgivenby
formula:
.TCCOG
(6)
3 ALGORITHMFORVESSEL’SDRIFT
CALCULATION
Presentedalgorithm consists of three parts: the
initialization, drift estimation and true heading
updating,seefigure4.
391
Set the initial position
),(
AA
A
START
Set the position of
),,(),,(
2211
21 GGGG
GG
END
Data:
,
A
t
satellite aerials’ positions
),,(
111
A ),,(
222
A
),,(
333
A ),,(
444
A
assume step
,t
,:
12
ttt
Data: actual
satellite aerials’
position
),,(
22
2 GG
G
Determine covered sea
route
G
d
(3-4),
I
N
I
T
I
A
L
I
Z
A
T
I
O
N
Estimate the vessel’s
course over ground
COG (5)
Estimate the angle
of total drift
TCCOG
(6)
BG
2
?
Is TC the
same?
ttt
22
:
Assume position
of point
2
G
as initial
21
: GG
Change start
position to
2
G
,:,:
22
GAGA
Correct true heading TC
D
R
I
F
T
E
S
T
I
M
A
T
I
O
N
T
R
U
E
H
E
A
D
I
N
G
U
P
D
A
T
E
Determine true heading
TC (1),
,:
1 A
tt
,:,:
11
AGAG
Do correct TC on
basis of position
A and B?
Set the final position B
Data:
),,(
BB
B
N
OYES
YES
YES
21
: tt
N
O
N
O
Figure4.Blockdiagramfortrueheadingandangleofvessel’stotaldriftcalculation
392
In the initial part all necessary data should be
giveni.e.satelliteaerials’positionsontheshipboard
at starting moment and final position that is a
destinationofavessel.Onthebasisofthesedatathe
trueheadingiscalculatedasithasbeenpresentedin
Section 2.
Next the procedure of determining the
vessel’scourseovergroundandangleoftotaldriftis
repeatedineachloopaftertimestep
.t
Theprocess
ends after reaching (getting) the destination that is
positionB. In each step the true heading of a vessel
mightbecorrectedtakingintoaccountactualvessel’s
position, destination and estimated angle of total
drift. Application is written in Java language using
SSJV2.1.3.Library.Theprogramwindow
forreading
initialdataisgiveninfigure5.
Figure5.Programwindowforreadinginitialdata
TheinitialpositionAcanbecountedfromsatellite
aerials’positionsthatshouldbeloadedfromsatellite
navigationsystem.ThefinalpositionBcanbegiven
bytheuser howeveritis possible toomitit. In that
caseit is impossible to correct the true heading of a
vessel on
basis of actual vessel position and
destination. The remaining part of the process does
notchange.
4 CONCLUSION
1 Presented above simple algorithm for continuous
monitoring in time the actual heading of a ship
movements can be effectively used for asses the
courseovergroundanddeterminethetotaldrift
of
thevessel.
2 Designated algorithm provides following
functions:
monitoring and assessment of navigation
processes,
presentingcurrentdriftoftheship,
helpinginroutedetermination,
supportingnavigationdecisions.
3 The algorithm is developed to aid the officer on
thewatchintheprocessofconductingnavigation
in
restrictedwaters.
4 Applicationofpresentedsystemwillcontributeto
increasesafetyonnavigationinpilotingareas.
5 The accuracy of determining true heading and
courseovergrounddependsonaccuracyofgiven
aerials’positions.Thelengthbases
L
d
,
B
d
used
todeterminevessel’strueheadinganddriftangel
have also influence on computation accuracy
[5][7].
REFERENCES
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Dynamic positioning system based on Kalman filtering and
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135‐163,1980.
[2]FossenT.I., PerezT.: Kalman Filtering for positioning and
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Systems
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[3]FossenT.I.,Strand J.P.: Nonlinear passive weather optimal
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[4]Jurdziński M.: Planowanie nawigacji wżegludze
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[5]Jurdziński M.: Możliwości uzyskania ciągłych wskazań
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[6]Sorensen A.J., Fossen T.I., Strand J.P.: Design of a
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‐Hawary, Ed. Boca Raton,
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